Macromolecules 1991,24, 1641-1647
1641
A Generalized Kinetic Model for Radical-Initiated Template
Polymerizations in Dilute Template Systems Y. Yong Tan' and Gert 0. R. Alberda van Ekenstein Laboratory of Polymer Chemistry, State University of Groningen, Nijenborgh 16, 9747 AG Groningen, The Netherlands Received December 8,1989;Revised Manuscript Received May 22, 1990 ABSTRACT A generalized kinetic model for dilute radical template polymerizations involving preferential monomer adsorptionby the template and following classical kinetics is described. By simulation,the influence of preferential monomer adsorption and of various rate constants pertaining to complexation, template propagation, and template termination of growing chain radicals on the rate enhancement induced by a template waa examined as a function of template concentration. This model has been applied to some known template polymerization systems. For some of these, template rate constants could be estimated by curve fitting to experimentallydetermined polymerization rate vs template concentration plots. 1. Introduction For many years, we have been examining radical polymerization systems in which chain propagation takes place along template macromolecules. As compared to conventional polymerization, such a propagation mode may lead to changes in polymerization kinetics and in structural features of the polymers formed. With regard to kinetics and mechanism, template systems have been classified into two types, which we called type I and type 11,' according to complete or no preadsorption (stoichiometric complexation) of monomer by (with) the template present in excess (expressed in base moles). Thus, type I leads to propagation of template-bound ("daughter") chain radicals with adsorbed monomer ("zip" reaction), whereas type I1 to that with free monomer ("pick-up" reaction). Actually, in most template polymerization systems, adsorption of monomer occurs to varying degrees depending on the kind of interaction between the template and the monomer and on the reaction conditions, which may be characterized by a simple adsorption equilibrium constant KM,which is assumed to be of the Langmuir type. Template polymerization of vinyl monomers is generally performed in a suitable inert solvent with an initiator like azoisobutyronitrile (AIBN). If K M has some finite value, indicating preferential monomer adsorption by the template, the following consecutive steps may be discerned: (1)initiation of monomer in solution, (2) initial propagation in solution, (3) complexation of (short) chain radicals with template macromolecules owing to cooperative specific interaction, (4) propagation along the template with either preadsorbed monomer or monomer from solution, and (5)termination. To interpret the kinetic results, simple models have been used based on either a pure type I (KM= 03) mechanism or a pure type I1 (KM N 0) mechanism. Recently, Smid3proposed a generalized model incorporating a finite KM,which was applied successfullyto the template polymerization of methacrylic acid along poly(2-~inylpyridine).~~ The purpose of this paper is to show how by computer simulation the different kinetic parameters would affect the template polymerization at constant initial monomer concentration and to analyze the outcome. Furthermore, examples will be given to demonstrate the application of this generalized model to some template polymerization systems extracted from the literature.
guished, viz. on the template macromolecules ("the template") and in the surrounding medium ("the solution"). Moreover, there are reactions at the interface of both loci. The generalized kinetic model may then be represented by the following scheme representing the sequence of reaction steps as already mentioned in the Introduction.
A. reaction steps in solution (1)initiator decomposition
kd
I
2R'
(2) initiation
(3) blank propagation
-
kPB
+ Mf
"B,n
(4)blank termination
"B,n+l
ktgB
'*B,n
+ p'B,in
-D
B'
B. complexations (1)monomer adsorption KM
Mf
+ T 2 MT
(2) radical complexation kc 'OB,"
+
'*T,n
(3) polymer complexation kc
PB+T-PT C. reaction steps on the template (1)template propagation
2. Kinetic Model
When a template system is considered, two loci where polymerization reactions take place should be distin-
(M = Mfor MT,depending on the instantaneous situation)
Macromolecules, Vol. 24, No. 7, 1991
1642 Tan and Alberda van Ekenstein
with
(2) template-template termination
TB
being the average lifetime of the blank radicals
(8) The composite rate constant k,,~,which is dependent on the free monomer concentration, is given by 7B =
(3) cross-termination
For the sake of brevity, propagation and termination proceeding in the solution and on the template are given the predicates "blank" (i.e., nontemplate) and "template", respectively. Mf signifies the monomer in the solution, whereas MT is the monomer adsorbed on the template. The following remarks should be made: (1) The complexation of living and dead polymers with template macromolecules is, strictly speaking, an equilibrium process. However, its equilibrium constant will rise rapidly with chain length because of the cooperativity of interacting forces,all the more if there is preferential adsorption of monomer. The back-reaction (decomplexation) is therefore neglected. Of course, k, will still depend on the chain length n of the complexing radicals (or preterminated chains) in the sense that k, would decrease with larger n due to diffusion. In order not to complicate matters, it is assumed that k, represents an average constant quantity and that a proportionate fraction of chains with different n's is complexed. (2) The template propagation along each chain in fact consists of a combination of the addition of either adsorbed monomer ("zip" ) free propagation: POT,,,+ MT with rate constant k , ~ or monomer ("pick-up" propagation: P'T,n + Mf with rate constant k , , d depending on the situation at hand. (3) Reactions at the template-solution interface not only involve the complexation but also termination between template-bound and free polymer radicals (cross-termination). It should be reminded that all kinds of termination reactions are actually diffusion controlled. For the sake of simplicity, its effect will be disregarded. (4) Chaintransfer reactions to monomer or solvent as well as to template are assumed to be absent. Based on the above scheme and assuming termination of blank radicals, P'B, by combination only and steady state of [R'], i.e., d[R']/dt = 0, the complete set of equations can be given by
Ri = 2fk,[I]
(1) (or @Iain the case of photoinitiation with @ = quantum yield and I , = intensity of absorbed light)
d [ P ' ~ ] / d t= Ri - ~ ~ ~ , B B [ P-' B ] ' k,BTIP'Bl
d[P'Tl/dt = kc[P'Bl [TI - kt,BT[p'Bl
- k,[P'Bl [TI (2) -
2kt,m[P'T]2 (3) -d[M]/dt = R, = R,,B + R,,T = (~,,B[P'B]+ Ap,TIP'Tl)[Mfl (4) d[PBl/dt = kt,BB[P'B12 - kc[PBl[Tl
(5)
-d[T]/dt = ~V&,[PB][T]+ VgkC[P*~][T] + Ap,T[p'Tl [Mfl (6) The kinetic chain length of the blank radicals is "B
= kp,BIMflTB
(7)
where
with Q = KM([T]- [MI) + 1and [MI being the sum of free and adsorbed monomer concentrations. It is assumed that k , I is independent of the array length of monomer on the template sites. Moreover, it is assumed that all constants are independent of template concen~ [Mt] changes with [TI. tration, except of course k p , since If KM is very large and [MI0 > [T]o, then KM[M~] >> 1, K M ~ , , I I [ M>>~ k,,r, ] ~ and (9) simplifies to k p , ~ kp,l/[Mf]. On introduction into (4), we get the rate for a type I po+fkp,I[P*T] ] with lymerization system, R, = k p ~ [ P * ~ ] [ M [Mflo= [MI0 - [Tlo. When [TI0 = [Mlo, [Mfloreduces to zero and R, becomes R , I = kp,I[P*T]. If KMis very small, then
